%latex.default(object = result, title = "", file = paste0("tables/",     filename, ".tex"), label = paste0("tb_", type), caption = caption,     insert.bottom = note, first.hline.double = FALSE, rowname = rownames,     cgroup = c("$n = 200$", "", "$n = 1000$", "", "$n = 200$",         "", "$n = 1000$"), n.cgroup = c(2, 1, 2, 2, 2, 1, 2),     cgroupTexCmd = "", colheads = clabels, rgroup = c("Correct PS model",         "Misspecified PS model"), n.rgroup = c(rep(nrow(res1),         2)), longtable = FALSE, center = "centering")%
\begin{table}[!tbp]
\caption{Simulation results: Linear outcome model 1\label{tb_linear1}} 
{\centering
\begin{tabular}{lrrcrcrrcrrcrrcrcrr}
\hline
\multicolumn{1}{l}{\ }&\multicolumn{2}{c}{\ $n = 200$}&\multicolumn{1}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{2}{c}{\ $n = 1000$}&\multicolumn{1}{c}{\ }&\multicolumn{2}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{2}{c}{\ $n = 200$}&\multicolumn{1}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{2}{c}{\ $n = 1000$}\tabularnewline
\cline{2-3} \cline{7-8} \cline{13-14} \cline{18-19}
\multicolumn{1}{l}{}&\multicolumn{1}{c}{Bias}&\multicolumn{1}{c}{RMSE}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{Bias}&\multicolumn{1}{c}{RMSE}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{Bias}&\multicolumn{1}{c}{RMSE}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{Bias}&\multicolumn{1}{c}{RMSE}\tabularnewline
\hline
{\bfseries Correct PS model}&&&&&&&&&&&&&&&&&&\tabularnewline
~~\textbf{nDBW}&$ -0.60$&$  2.86$&&$$&&$ -0.09$&$  1.33$&&$$&$$&&$ 0.76$&$ 2.95$&&$$&&$ 0.03$&$ 1.34$\tabularnewline
~~MLE&$ -0.27$&$ 11.61$&&$$&&$ -0.04$&$  4.90$&&$$&$$&&$-0.03$&$ 7.67$&&$$&&$-0.02$&$ 2.82$\tabularnewline
~~CBPS&$  1.94$&$  4.54$&&$$&&$  0.37$&$  1.76$&&$$&$$&&$ 2.04$&$ 4.73$&&$$&&$ 0.30$&$ 1.78$\tabularnewline
~~Calibrated weighting&$  0.06$&$  2.57$&&$$&&$  0.00$&$  1.15$&&$$&$$&&$ 0.04$&$ 2.60$&&$$&&$-0.06$&$ 1.16$\tabularnewline
~~Entropy balancing&$  0.06$&$  2.57$&&$$&&$ -0.01$&$  1.15$&&$$&$$&&$ 0.04$&$ 2.60$&&$$&&$-0.06$&$ 1.16$\tabularnewline
~~True propensity score&$  0.05$&$ 23.28$&&$$&&$  0.39$&$ 10.74$&&$$&$$&&$-0.45$&$17.95$&&$$&&$-0.26$&$ 8.12$\tabularnewline
~~Unweighted&$ -9.78$&$ 10.39$&&$$&&$ -9.97$&$ 10.09$&&$$&$$&&$10.05$&$10.68$&&$$&&$ 9.95$&$10.07$\tabularnewline
~~\textbf{nDBW DR}&$  0.54$&$  2.89$&&$$&&$  0.17$&$  1.31$&&$$&$$&&$ 0.74$&$ 2.80$&&$$&&$ 0.09$&$ 1.20$\tabularnewline
~~MLE DR&$  0.36$&$  3.65$&&$$&&$  0.01$&$  1.74$&&$$&$$&&$ 0.44$&$ 3.74$&&$$&&$ 0.00$&$ 1.76$\tabularnewline
~~CBPS DR&$  0.49$&$  3.25$&&$$&&$  0.07$&$  1.59$&&$$&$$&&$ 0.38$&$ 3.08$&&$$&&$ 0.02$&$ 1.46$\tabularnewline
~~Calibrated weighting DR&$  0.54$&$  2.97$&&$$&&$  0.12$&$  1.41$&&$$&$$&&$ 0.42$&$ 2.74$&&$$&&$ 0.04$&$ 1.22$\tabularnewline
~~Entropy balancing DR&$  1.15$&$  3.16$&&$$&&$  0.91$&$  1.64$&&$$&$$&&$ 1.40$&$ 3.10$&&$$&&$ 1.11$&$ 1.66$\tabularnewline
~~True propensity score DR~~&$  0.37$&$  3.57$&&$$&&$  0.04$&$  1.81$&&$$&$$&&$ 0.62$&$ 4.08$&&$$&&$ 0.05$&$ 1.96$\tabularnewline
~~Imputation&$ -0.55$&$  3.32$&&$$&&$ -0.82$&$  1.74$&&$$&$$&&$ 4.93$&$ 5.79$&&$$&&$ 4.90$&$ 5.08$\tabularnewline
\hline
{\bfseries Misspecified PS model}&&&&&&&&&&&&&&&&&&\tabularnewline
~~\textbf{nDBW}&$ -3.21$&$  4.77$&&$$&&$ -3.70$&$  4.08$&&$$&$$&&$ 3.48$&$ 4.64$&&$$&&$ 1.10$&$ 1.75$\tabularnewline
~~MLE&$ 20.93$&$143.01$&&$$&&$ 44.47$&$292.98$&&$$&$$&&$ 0.54$&$ 6.75$&&$$&&$ 0.53$&$ 2.51$\tabularnewline
~~CBPS&$  1.03$&$  4.84$&&$$&&$ -2.01$&$  2.94$&&$$&$$&&$ 6.18$&$ 7.55$&&$$&&$ 3.86$&$ 4.19$\tabularnewline
~~Calibrated weighting&$ -2.14$&$  3.83$&&$$&&$ -2.76$&$  3.14$&&$$&$$&&$ 2.31$&$ 3.70$&&$$&&$ 2.23$&$ 2.58$\tabularnewline
~~Entropy balancing&$ -1.52$&$  3.56$&&$$&&$ -1.95$&$  2.46$&&$$&$$&&$ 3.79$&$ 4.80$&&$$&&$ 3.77$&$ 4.00$\tabularnewline
~~True propensity score&$  0.21$&$ 23.15$&&$$&&$ -0.28$&$ 10.51$&&$$&$$&&$ 0.18$&$18.23$&&$$&&$-0.08$&$ 8.37$\tabularnewline
~~Unweighted&$-10.02$&$ 10.64$&&$$&&$ -9.97$&$ 10.10$&&$$&$$&&$ 9.92$&$10.51$&&$$&&$10.01$&$10.14$\tabularnewline
~~\textbf{nDBW DR}&$ -1.98$&$  3.73$&&$$&&$ -2.61$&$  2.99$&&$$&$$&&$ 2.49$&$ 3.81$&&$$&&$ 1.79$&$ 2.18$\tabularnewline
~~MLE DR&$ -5.97$&$ 22.52$&&$$&&$-16.30$&$129.23$&&$$&$$&&$ 3.11$&$ 4.49$&&$$&&$ 3.07$&$ 3.39$\tabularnewline
~~CBPS DR/BRDR&$ -2.73$&$  4.36$&&$$&&$ -3.57$&$  3.97$&&$$&$$&&$ 3.07$&$ 4.39$&&$$&&$ 3.33$&$ 3.63$\tabularnewline
~~Calibrated weighting DR&$ -2.14$&$  3.83$&&$$&&$ -2.76$&$  3.14$&&$$&$$&&$ 2.31$&$ 3.70$&&$$&&$ 2.23$&$ 2.58$\tabularnewline
~~Entropy balancing DR&$ -1.52$&$  3.56$&&$$&&$ -1.95$&$  2.46$&&$$&$$&&$ 3.79$&$ 4.80$&&$$&&$ 3.77$&$ 4.00$\tabularnewline
~~True propensity score DR~~&$  0.31$&$  3.66$&&$$&&$  0.09$&$  1.77$&&$$&$$&&$ 0.47$&$ 4.09$&&$$&&$ 0.12$&$ 1.97$\tabularnewline
~~Imputation&$ -0.62$&$  3.39$&&$$&&$ -0.82$&$  1.70$&&$$&$$&&$ 4.84$&$ 5.67$&&$$&&$ 4.96$&$ 5.14$\tabularnewline
\hline
\end{tabular}}
\parbox{0.99\textwidth}
		{Notes: This simulation compares the performance of various methods 
		for estimating propensity scores and (inverse probability) weights 
		by investigating combinations of six versions of the true outcome model 
		(linear~1, linear~2, quadratic~1, quadratic~2, exponential~1, and exponential~2)
		and two versions of coefficients for the true propensity score model (type~A and B)
		with the two different numbers of observations ($n = 200$ and $n = 1000$).
		For each estimation method, I use two propensity score model specifications 
		(correct and misspecified) and report the bias and RMSE for each in the table.}\end{table}
